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$%M. Kabanava, Tempered Radon measures, Rev. Mat. Complut. 21 (2008), no. 2, 553–564.%$

Tempered Radon Measures
Maryia KABANAVA
Mathematical Institute
Friedrich Schiller University Jena
D-07737 Jena, Germany
kabanova@minet.uni-jena.de
Received: December 11, 2007
Accepted: January 1, 2008

ABSTRACT

A tempered Radon measure is a σ  -finite Radon measure in  n
ℝ  which generates a tempered distribution. We prove the following assertions. A Radon measure μ  is tempered if, and only if, there is a real number β  such that       2β2
(1+ |x| ) μ  is finite. A Radon measure is finite if, and only if, it belongs to the positive cone +
B01∞ (ℝn )  of B01∞(ℝn)  . Then μ(ℝn)~ ∥μ|B01∞ (ℝn )∥ (equivalent norms).

Key words: Radon measure, tempered distributions, Besov spaces.
2000 Mathematics Subject Classification:
42B35, 28C05.